chapter 12 leverage and capital structure
TRANSCRIPT
Microsoft PowerPoint - Presentation1 [Compatibility Mode]Part one :
Leverage
Leverage
Refers to the effects that fixed costs have on the returns that shareholders earn; higher leverage generally results in higher but more volatile returns.
Types of leverage include:
4/16/2012 4Managerial Finance_An-Najah University
- Variable selling and administrative expenses
= Contribution margin
Contribution Margin Income Statement Format
-
- Fixed selling and administrative expenses
= Net operating income or loss
A contribution margin income statement is an income statement in which all
variable expenses are deducted from sales to arrive at a contribution margin,
from which all fixed expenses are then subtracted to arrive at the net operating
income or loss for the period.
4/16/2012 5Managerial Finance_An-Najah University
Breakeven Point
Sales Revenue (P × Q)
Less: Fixed Operating Expenses - FC__
Earning before Interest and Taxes EBIT
P = sales price per unit
Q = sales quantity in units
FC = fixed operating costs per period
VC = variable operating costs per unit
EBIT = operating profit
Rewriting the algebraic calculations
4/16/2012 6Managerial Finance_An-Najah University
Operating Breakeven Point is:
The level of sales necessary to cover all operating costs; the point at
which EBIT =$0.
To determine the operating breakeven point let EBIT =$0.
QO.B.E (P - VC) = FC
QO.B.E : is operating breakeven point in Unit Sales
(QO.B.E x P ) : is operating breakeven point in dollar Sales 4/16/2012 7Managerial Finance_An-Najah University
How changes in FC, P , FC will change Q O.B.E
______Variable_______ Change Effect on Q O.B.E.
FC
Decrease Decrease
Decrease Increase
Decrease Decrease
Q Sales > Q O.B.E
Q Sales = Q O.B.E
operating leverage
The use of fixed operating costs to magnify the effects of
changes in sales on the firm’s earnings before interest and
taxes.
Sales
EBIT
Measuring the Degree of Operating Leverage : Equation 1 Degree of Operating Leverage (DOL)
The numerical measure of the firm’s operating leverage.
DOL = Percentage change in EBIT
Percentage change in sales
DOL = % EBIT
For any real number a, the absolute value of a, denoted by |a| is itself if a ≥ 0, and -a if a < 0.
Thus |a| is positive expect when a = 0
DOL = % EBIT
% EBIT > % sales
As long as DOL > 1 Operating Leverage exists
If DOL = 1 then Operating Leverage does not exist 4/16/2012 11Managerial Finance_An-Najah University
Measuring the Degree of Operating Leverage : Equation 2
DOL at base sales level Q = Q * (P - VC)
Q * (P - VC) - FC
DOL at base sales level Q = Q * Unit Contribution Margin
Q * Unit Contribution Margin - FC
The higher the Fixed Cost the higher the Degree of Operating Leverage
4/16/2012 12Managerial Finance_An-Najah University
DOL at base dollar sales TR = Sales – Total Variable Cost
Sales– Total Variable Cost – FC
DOL at base sales level Q = Q * (P - VC)
Q * (P - VC) - FC
TR – TVC – FC =
TVC= Q x VC
TCM = Q x Unit Contribution Margin = Q x (P-VC)
EBIT = (Q x P) – (Q x VC) – FC = Q * (P - VC) - FC
4/16/2012 13Managerial Finance_An-Najah University
financial leverage
The use of fixed financial costs to magnify the effects of
changes in earnings before interest and taxes on the firm’s
earnings per share.
The numerical measure of the firm’s financial leverage.
The two most common fixed financial costs are:
(1) interest on debt (I)
(2) preferred stock dividends (PD)
4/16/2012 14Managerial Finance_An-Najah University
DFL = Percentage change in EPS
Percentage change in EBIT
EBIT – Fixed Financial Cost
EBIT – I – [ PD x (1- T) ] 1
DFL at base level EBIT = EBIT
EBIT – I – PD x 1
(1- T)
after tax to before tax, because
all other items are before tax
4/16/2012 15Managerial Finance_An-Najah University
DFL at base level EBIT = EBIT
EBIT – Fixed Financial Cost
EBIT – I – PD x 1 DFL at base level EBIT =
EBIT – I – PD x 1
(1- T)
[ Q * (P - VC) – FC] – I – PD x 1
(1- T)
The use of fixed costs, both operating and financial, to
magnify the effects of changes in sales on the firm’s
earnings per share.
The numerical measure of the firm’s total leverage.
DTL = DOL × DFLDTL = DOL × DFL
4/16/2012 17Managerial Finance_An-Najah University
DTL = Percentage change in EPS
Percentage change in Sales =
DTL at base level Q = [ Q * (P - VC)]
DTL at base level Q = [ Q * (P - VC) – FC] – I – PD x 1
(1- T)
EBIT – Fixed Financial Costs
4/16/2012 18Managerial Finance_An-Najah University
DFL = EBIT
% Sales
= % EBIT
% Sales ×
% EPS
% EBIT
E–1
Canvas Reproductions has fixed operating costs of $12,500 and variable operating costs
of $10 per unit and sells its paintings for $25 each. At what level of unit sales will the
company break even in terms of EBIT?
Given :
QO.B.E = ??
QO.B.E = 833.33 Unit
E–2
The Great Fish Taco Corporation currently has fixed operating costs of $15,000, sells its
premade tacos for $6 per box, and incurs variable operating costs of $2.50 per box. If the firm
has a potential investment that would simultaneously raise its fixed costs to $16,500 and allow
it to charge a per-box sale price of $6.50 due to better-textured tacos, what will the impact be on
its operating breakeven point in boxes?
Given :
P1= $6 per unit
VC= $2.5 per unit
QO.B.E 1= 4285.7 units QO.B.E 1= 4125units
Impact of changes in fixed operating cost and in price per unit on operating breakeven point:
QO.B.E 1 = 4285.7 > QO.B.E 2 = 4125
which means that even though there was an increase in fixed operating costs that have a positive effect
on breakeven point in case 2, but there was also an increase in price per unit that have a negative effect
on breakeven point, and the negative effect had a larger impact than the positive one.
E–3
Chico’s has sales of 15,000 units at a price of $20 per unit. The firm incurs fixed operating
costs of $30,000 and variable operating costs of $12 per unit. What is Chico’s degree of
operating leverage (DOL) at a base level of sales of 15,000 units?
DOL = Total Contribution Margin
FC= $30,000
DOL = 1.33
E–4
Parker Investments has EBIT of $20,000, interest expense of $3,000, and preferred dividends of
$4,000. If it pays taxes at a rate of 38%, what is Parker’s degree of financial leverage (DFL) at a base
level of EBIT of $20,000?
Given :
PD= $4,000
T= 38%
DFL= ?? DFL =
( 1-.38)
P–1
Kate Rowland wishes to estimate the number of flower arrangements she must sell at
$24.95 to break even. She has estimated fixed operating costs of $12,350 per year and
variable operating costs of $15.45 per arrangement. How many flower arrangements must
Kate sell to break even on operating costs?
Given :
P-2
Given the price and cost data shown in the accompanying table for each of the three firms, F, G, and H,
answer the questions that follow.
a. What is the operating breakeven point in units for each firm?
b. How would you rank these firms in terms of their risk?
FC From least risky to most risky: F and
4/16/2012 Managerial Finance_An-Najah University 25
a.
G are of equal risk, then H. It is
important to recognize that operating
leverage is only one measure of risk.
Firm F = Firm G
P-3
Fine Leather Enterprises sells its single product for $129.00 per unit. The firm’s fixed
operating costs are $473,000 annually, and its variable operating costs are $86.00 per unit. Find
the firm’s operating breakeven point in units.
Given :
VC= $86 per unit
P-4
Breakeven analysis Barry Carter is considering opening a music store. He wants to estimate the number of CDs he
must sell to break even. The CDs will be sold for $13.98 each, variable operating costs are $10.48 per CD, and
annual fixed operating costs are $73,500.
a. Find the operating breakeven point in number of CDs.
b. Calculate the total operating costs at the breakeven volume found in part a.
c. If Barry estimates that at a minimum he can sell 2,000 CDs per month, should he go into the music business?
d. How much EBIT will Barry realize if he sells the minimum 2,000 CDs per month noted in part c?
500,73$ ==a. per year
( ) CDs 000,21
= FC + (Q x VC)
24,000 – 21,000 = 3,000 unit of CDs above breakeven point.
Barry sales exceeds the operating breakeven by 3,000 records per year.
Barry should go into the CD business.
a.
b.
c.
- Total Variable cost (VC x Q) ($10.48 x 24,000)
- FC ( FC ) ($73,500)
P-6
JWG Company publishes Creative Crosswords. Last year the book of puzzles sold for $10 with variable operating
cost per book of $8 and fixed operating costs of $40,000. How many books must JWG sell this year to achieve
the breakeven point for the stated operating costs, given the following different circumstances?
a. All figures remain the same as for last year.
b. Fixed operating costs increase to $44,000; all other figures remain the same.
c. The selling price increases to $10.50; all costs remain the same as for last year.
d. Variable operating cost per book increases to $8.50; all other figures remain the same.
e. What can you conclude from the previous results?
a. ( ) book. 20,000
e.
a.
b.
c.
Decrease Decrease
Decrease Increase
Decrease Decrease
P-9
Grey Products has fixed operating costs of $380,000, variable operating costs of $16 per unit, and a selling
price of $63.50 per unit.
a. Calculate the operating breakeven point in units.
b. Calculate the firm’s EBIT at 9,000, 10,000, and 11,000 units, respectively.
c. With 10,000 units as a base, what are the percentage changes in units sold and EBIT as sales
move from the base to the other sales levels used in part b?
d. Use the percentages computed in part c to determine the degree of operating leverage (DOL).
e. Use the formula for degree of operating leverage to determine the DOL at 10,000 units.
4/16/2012 Managerial Finance_An-Najah University 29
a. ( ) unit. 8,000
FC Q
Level of sales in units 9,000 units 10,000 units 11,000 units
$ Sales (Q × P) $571,500 $635,000 $698,500
- Variable costs (Q × VC) (144,000) (160,000) (176,000)
- Fixed costs (380,000) (380,000) (380,000)
= EBIT $ 47,500 $ 95,000 $142,500
Units base
11,000 units
Change in Unit Sales 9,000 – 10,000 = - 1,000 0 11,000 – 10,000 = + 1,000
% Change in Sales 9,000 – 10,000 = - 10%
10,000
95,000 EBIT
Change in EBIT 47,500 – 95,000 = -$47,500 0 142,500 – 95,000 = +$47,500
% Change in EBIT 47,500 – 95,000 = - 50%
95,000
- 50 % = 5
[ ] [ ] ][VC)-(PQ
Southland Industries has $60,000 of 16% (annual interest) bonds outstanding, 1,500 shares of preferred
stock paying an annual dividend of $5 per share, and 4,000 shares of common stock outstanding.
Assuming that the firm has a 40% tax rate, compute earnings per share (EPS) for the following levels of
EBIT:
Number of shares of common stock outstanding
4/16/2012 Managerial Finance_An-Najah University 32
(a) (b) (c)
Net profits before taxes $15,000 $21,000 $25,400
Less: Taxes 6,000 8,400 10,160
Net profit after taxes $9,000 $12,600 $15,240
Less: Preferred dividends 7,500 7,500 7,500
Earnings available to common shareholders $1,500 $5,100 $7,740
EPS (4,000 shares) $0.375 $1.275 $1.935
P-12
Northwestern Savings and Loan has a current capital structure consisting of $250,000 of 16% (annual interest)
debt and 2,000 shares of common stock. The firm pays taxes at the rate of 40%.
a. Using EBIT values of $80,000 and $120,000, determine the associated earnings per share (EPS).
b. Using $80,000 of EBIT as a base, calculate the degree of financial leverage (DFL).
c. Rework parts a and b assuming that the firm has $100,000 of 16% (annual interest) debt and 3,000
shares of common stock.
Less: Taxes (40%) 16,000 32,000
a.
= % 16 × 250,000 = $ 40,000
Net profit after taxes $24,000 $48,000
EPS (2,000 shares) $12.00 $24.00
×
Less: Taxes (40%) 25,600 41,600
Net profit after taxes $38,400 $62,400
EPS (3,000 shares) $12.80 $20.80
Total interest amount = % annual interest × total debt value
= % 16 × 100,000 = $ 16,000
×
P-15
Play-More Toys produces inflatable beach balls, selling 400,000 balls per year. Each ball produced has a
variable operating cost of $0.84 and sells for $1.00. Fixed operating costs are $28,000. The firm has annual
interest charges of $6,000, preferred dividends of $2,000, and a 40% tax rate.
a. Calculate the operating breakeven point in units.
b. Use the degree of operating leverage (DOL) formula to calculate DOL.
c. Use the degree of financial leverage (DFL) formula to calculate DFL.
d. Use the degree of total leverage (DTL) formula to calculate DTL. Compare this to the product of DOL
and DFL calculated in parts b and c.
Q = FC ÷ (P - VC) Q = $28,000 ÷ ($1 - $.84) = 175,000 unit a.
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[ ] [ ] FCVC)-(PQ
EBIT = $400,000 - $28,000 - $336,000
×
[ ] 40.2
667,26$
000,64$
$9,333-$28,000-$64,000
The two formulas give the same result.
P-16
Firm R has sales of 100,000 units at $2.00 per unit, variable operating costs of $1.70 per unit, and fixed operating
costs of $6,000. Interest is $10,000 per year. Firm W has sales of 100,000 units at $2.50 per unit, variable
operating costs of $1.00 per unit, and fixed operating costs of $62,500. Interest is $17,500 per year. Assume that
both firms are in the 40% tax bracket.
a. Compute the degree of operating, financial, and total leverage for firm R.
b. Compute the degree of operating, financial, and total leverage for firm W.
c. Compare the relative risks of the two firms.
d. Discuss the principles of leverage that your answers illustrate.
a. For Firm R :
[ ] [ ]
[ ] [ ]
b. For Firm W :
DTL w = 1.71 x 1.25 = 2.14
c. Firm R has less operating (business) risk but more financial risk than Firm W.
d. Two firms with differing operating and financial structures may be equally leveraged. Since
total leverage is the product of operating and financial leverage, each firm may structure
Leverage
Refers to the effects that fixed costs have on the returns that shareholders earn; higher leverage generally results in higher but more volatile returns.
Types of leverage include:
4/16/2012 4Managerial Finance_An-Najah University
- Variable selling and administrative expenses
= Contribution margin
Contribution Margin Income Statement Format
-
- Fixed selling and administrative expenses
= Net operating income or loss
A contribution margin income statement is an income statement in which all
variable expenses are deducted from sales to arrive at a contribution margin,
from which all fixed expenses are then subtracted to arrive at the net operating
income or loss for the period.
4/16/2012 5Managerial Finance_An-Najah University
Breakeven Point
Sales Revenue (P × Q)
Less: Fixed Operating Expenses - FC__
Earning before Interest and Taxes EBIT
P = sales price per unit
Q = sales quantity in units
FC = fixed operating costs per period
VC = variable operating costs per unit
EBIT = operating profit
Rewriting the algebraic calculations
4/16/2012 6Managerial Finance_An-Najah University
Operating Breakeven Point is:
The level of sales necessary to cover all operating costs; the point at
which EBIT =$0.
To determine the operating breakeven point let EBIT =$0.
QO.B.E (P - VC) = FC
QO.B.E : is operating breakeven point in Unit Sales
(QO.B.E x P ) : is operating breakeven point in dollar Sales 4/16/2012 7Managerial Finance_An-Najah University
How changes in FC, P , FC will change Q O.B.E
______Variable_______ Change Effect on Q O.B.E.
FC
Decrease Decrease
Decrease Increase
Decrease Decrease
Q Sales > Q O.B.E
Q Sales = Q O.B.E
operating leverage
The use of fixed operating costs to magnify the effects of
changes in sales on the firm’s earnings before interest and
taxes.
Sales
EBIT
Measuring the Degree of Operating Leverage : Equation 1 Degree of Operating Leverage (DOL)
The numerical measure of the firm’s operating leverage.
DOL = Percentage change in EBIT
Percentage change in sales
DOL = % EBIT
For any real number a, the absolute value of a, denoted by |a| is itself if a ≥ 0, and -a if a < 0.
Thus |a| is positive expect when a = 0
DOL = % EBIT
% EBIT > % sales
As long as DOL > 1 Operating Leverage exists
If DOL = 1 then Operating Leverage does not exist 4/16/2012 11Managerial Finance_An-Najah University
Measuring the Degree of Operating Leverage : Equation 2
DOL at base sales level Q = Q * (P - VC)
Q * (P - VC) - FC
DOL at base sales level Q = Q * Unit Contribution Margin
Q * Unit Contribution Margin - FC
The higher the Fixed Cost the higher the Degree of Operating Leverage
4/16/2012 12Managerial Finance_An-Najah University
DOL at base dollar sales TR = Sales – Total Variable Cost
Sales– Total Variable Cost – FC
DOL at base sales level Q = Q * (P - VC)
Q * (P - VC) - FC
TR – TVC – FC =
TVC= Q x VC
TCM = Q x Unit Contribution Margin = Q x (P-VC)
EBIT = (Q x P) – (Q x VC) – FC = Q * (P - VC) - FC
4/16/2012 13Managerial Finance_An-Najah University
financial leverage
The use of fixed financial costs to magnify the effects of
changes in earnings before interest and taxes on the firm’s
earnings per share.
The numerical measure of the firm’s financial leverage.
The two most common fixed financial costs are:
(1) interest on debt (I)
(2) preferred stock dividends (PD)
4/16/2012 14Managerial Finance_An-Najah University
DFL = Percentage change in EPS
Percentage change in EBIT
EBIT – Fixed Financial Cost
EBIT – I – [ PD x (1- T) ] 1
DFL at base level EBIT = EBIT
EBIT – I – PD x 1
(1- T)
after tax to before tax, because
all other items are before tax
4/16/2012 15Managerial Finance_An-Najah University
DFL at base level EBIT = EBIT
EBIT – Fixed Financial Cost
EBIT – I – PD x 1 DFL at base level EBIT =
EBIT – I – PD x 1
(1- T)
[ Q * (P - VC) – FC] – I – PD x 1
(1- T)
The use of fixed costs, both operating and financial, to
magnify the effects of changes in sales on the firm’s
earnings per share.
The numerical measure of the firm’s total leverage.
DTL = DOL × DFLDTL = DOL × DFL
4/16/2012 17Managerial Finance_An-Najah University
DTL = Percentage change in EPS
Percentage change in Sales =
DTL at base level Q = [ Q * (P - VC)]
DTL at base level Q = [ Q * (P - VC) – FC] – I – PD x 1
(1- T)
EBIT – Fixed Financial Costs
4/16/2012 18Managerial Finance_An-Najah University
DFL = EBIT
% Sales
= % EBIT
% Sales ×
% EPS
% EBIT
E–1
Canvas Reproductions has fixed operating costs of $12,500 and variable operating costs
of $10 per unit and sells its paintings for $25 each. At what level of unit sales will the
company break even in terms of EBIT?
Given :
QO.B.E = ??
QO.B.E = 833.33 Unit
E–2
The Great Fish Taco Corporation currently has fixed operating costs of $15,000, sells its
premade tacos for $6 per box, and incurs variable operating costs of $2.50 per box. If the firm
has a potential investment that would simultaneously raise its fixed costs to $16,500 and allow
it to charge a per-box sale price of $6.50 due to better-textured tacos, what will the impact be on
its operating breakeven point in boxes?
Given :
P1= $6 per unit
VC= $2.5 per unit
QO.B.E 1= 4285.7 units QO.B.E 1= 4125units
Impact of changes in fixed operating cost and in price per unit on operating breakeven point:
QO.B.E 1 = 4285.7 > QO.B.E 2 = 4125
which means that even though there was an increase in fixed operating costs that have a positive effect
on breakeven point in case 2, but there was also an increase in price per unit that have a negative effect
on breakeven point, and the negative effect had a larger impact than the positive one.
E–3
Chico’s has sales of 15,000 units at a price of $20 per unit. The firm incurs fixed operating
costs of $30,000 and variable operating costs of $12 per unit. What is Chico’s degree of
operating leverage (DOL) at a base level of sales of 15,000 units?
DOL = Total Contribution Margin
FC= $30,000
DOL = 1.33
E–4
Parker Investments has EBIT of $20,000, interest expense of $3,000, and preferred dividends of
$4,000. If it pays taxes at a rate of 38%, what is Parker’s degree of financial leverage (DFL) at a base
level of EBIT of $20,000?
Given :
PD= $4,000
T= 38%
DFL= ?? DFL =
( 1-.38)
P–1
Kate Rowland wishes to estimate the number of flower arrangements she must sell at
$24.95 to break even. She has estimated fixed operating costs of $12,350 per year and
variable operating costs of $15.45 per arrangement. How many flower arrangements must
Kate sell to break even on operating costs?
Given :
P-2
Given the price and cost data shown in the accompanying table for each of the three firms, F, G, and H,
answer the questions that follow.
a. What is the operating breakeven point in units for each firm?
b. How would you rank these firms in terms of their risk?
FC From least risky to most risky: F and
4/16/2012 Managerial Finance_An-Najah University 25
a.
G are of equal risk, then H. It is
important to recognize that operating
leverage is only one measure of risk.
Firm F = Firm G
P-3
Fine Leather Enterprises sells its single product for $129.00 per unit. The firm’s fixed
operating costs are $473,000 annually, and its variable operating costs are $86.00 per unit. Find
the firm’s operating breakeven point in units.
Given :
VC= $86 per unit
P-4
Breakeven analysis Barry Carter is considering opening a music store. He wants to estimate the number of CDs he
must sell to break even. The CDs will be sold for $13.98 each, variable operating costs are $10.48 per CD, and
annual fixed operating costs are $73,500.
a. Find the operating breakeven point in number of CDs.
b. Calculate the total operating costs at the breakeven volume found in part a.
c. If Barry estimates that at a minimum he can sell 2,000 CDs per month, should he go into the music business?
d. How much EBIT will Barry realize if he sells the minimum 2,000 CDs per month noted in part c?
500,73$ ==a. per year
( ) CDs 000,21
= FC + (Q x VC)
24,000 – 21,000 = 3,000 unit of CDs above breakeven point.
Barry sales exceeds the operating breakeven by 3,000 records per year.
Barry should go into the CD business.
a.
b.
c.
- Total Variable cost (VC x Q) ($10.48 x 24,000)
- FC ( FC ) ($73,500)
P-6
JWG Company publishes Creative Crosswords. Last year the book of puzzles sold for $10 with variable operating
cost per book of $8 and fixed operating costs of $40,000. How many books must JWG sell this year to achieve
the breakeven point for the stated operating costs, given the following different circumstances?
a. All figures remain the same as for last year.
b. Fixed operating costs increase to $44,000; all other figures remain the same.
c. The selling price increases to $10.50; all costs remain the same as for last year.
d. Variable operating cost per book increases to $8.50; all other figures remain the same.
e. What can you conclude from the previous results?
a. ( ) book. 20,000
e.
a.
b.
c.
Decrease Decrease
Decrease Increase
Decrease Decrease
P-9
Grey Products has fixed operating costs of $380,000, variable operating costs of $16 per unit, and a selling
price of $63.50 per unit.
a. Calculate the operating breakeven point in units.
b. Calculate the firm’s EBIT at 9,000, 10,000, and 11,000 units, respectively.
c. With 10,000 units as a base, what are the percentage changes in units sold and EBIT as sales
move from the base to the other sales levels used in part b?
d. Use the percentages computed in part c to determine the degree of operating leverage (DOL).
e. Use the formula for degree of operating leverage to determine the DOL at 10,000 units.
4/16/2012 Managerial Finance_An-Najah University 29
a. ( ) unit. 8,000
FC Q
Level of sales in units 9,000 units 10,000 units 11,000 units
$ Sales (Q × P) $571,500 $635,000 $698,500
- Variable costs (Q × VC) (144,000) (160,000) (176,000)
- Fixed costs (380,000) (380,000) (380,000)
= EBIT $ 47,500 $ 95,000 $142,500
Units base
11,000 units
Change in Unit Sales 9,000 – 10,000 = - 1,000 0 11,000 – 10,000 = + 1,000
% Change in Sales 9,000 – 10,000 = - 10%
10,000
95,000 EBIT
Change in EBIT 47,500 – 95,000 = -$47,500 0 142,500 – 95,000 = +$47,500
% Change in EBIT 47,500 – 95,000 = - 50%
95,000
- 50 % = 5
[ ] [ ] ][VC)-(PQ
Southland Industries has $60,000 of 16% (annual interest) bonds outstanding, 1,500 shares of preferred
stock paying an annual dividend of $5 per share, and 4,000 shares of common stock outstanding.
Assuming that the firm has a 40% tax rate, compute earnings per share (EPS) for the following levels of
EBIT:
Number of shares of common stock outstanding
4/16/2012 Managerial Finance_An-Najah University 32
(a) (b) (c)
Net profits before taxes $15,000 $21,000 $25,400
Less: Taxes 6,000 8,400 10,160
Net profit after taxes $9,000 $12,600 $15,240
Less: Preferred dividends 7,500 7,500 7,500
Earnings available to common shareholders $1,500 $5,100 $7,740
EPS (4,000 shares) $0.375 $1.275 $1.935
P-12
Northwestern Savings and Loan has a current capital structure consisting of $250,000 of 16% (annual interest)
debt and 2,000 shares of common stock. The firm pays taxes at the rate of 40%.
a. Using EBIT values of $80,000 and $120,000, determine the associated earnings per share (EPS).
b. Using $80,000 of EBIT as a base, calculate the degree of financial leverage (DFL).
c. Rework parts a and b assuming that the firm has $100,000 of 16% (annual interest) debt and 3,000
shares of common stock.
Less: Taxes (40%) 16,000 32,000
a.
= % 16 × 250,000 = $ 40,000
Net profit after taxes $24,000 $48,000
EPS (2,000 shares) $12.00 $24.00
×
Less: Taxes (40%) 25,600 41,600
Net profit after taxes $38,400 $62,400
EPS (3,000 shares) $12.80 $20.80
Total interest amount = % annual interest × total debt value
= % 16 × 100,000 = $ 16,000
×
P-15
Play-More Toys produces inflatable beach balls, selling 400,000 balls per year. Each ball produced has a
variable operating cost of $0.84 and sells for $1.00. Fixed operating costs are $28,000. The firm has annual
interest charges of $6,000, preferred dividends of $2,000, and a 40% tax rate.
a. Calculate the operating breakeven point in units.
b. Use the degree of operating leverage (DOL) formula to calculate DOL.
c. Use the degree of financial leverage (DFL) formula to calculate DFL.
d. Use the degree of total leverage (DTL) formula to calculate DTL. Compare this to the product of DOL
and DFL calculated in parts b and c.
Q = FC ÷ (P - VC) Q = $28,000 ÷ ($1 - $.84) = 175,000 unit a.
4/16/2012 Managerial Finance_An-Najah University 35
[ ] [ ] FCVC)-(PQ
EBIT = $400,000 - $28,000 - $336,000
×
[ ] 40.2
667,26$
000,64$
$9,333-$28,000-$64,000
The two formulas give the same result.
P-16
Firm R has sales of 100,000 units at $2.00 per unit, variable operating costs of $1.70 per unit, and fixed operating
costs of $6,000. Interest is $10,000 per year. Firm W has sales of 100,000 units at $2.50 per unit, variable
operating costs of $1.00 per unit, and fixed operating costs of $62,500. Interest is $17,500 per year. Assume that
both firms are in the 40% tax bracket.
a. Compute the degree of operating, financial, and total leverage for firm R.
b. Compute the degree of operating, financial, and total leverage for firm W.
c. Compare the relative risks of the two firms.
d. Discuss the principles of leverage that your answers illustrate.
a. For Firm R :
[ ] [ ]
[ ] [ ]
b. For Firm W :
DTL w = 1.71 x 1.25 = 2.14
c. Firm R has less operating (business) risk but more financial risk than Firm W.
d. Two firms with differing operating and financial structures may be equally leveraged. Since
total leverage is the product of operating and financial leverage, each firm may structure